English(EN) Linear Independence of Polynomial Compositions with Bounded Input Degree

数学论文通过多项式复合无关性证明神经网络可识别性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-16 04:00

本文利用有理曲线的变形和线性化方程核证明了Kohn、Marchetti、Massarenti和Mella的弱复合无关猜想。该证明利用黎曼-罗赫定理，从具有可控极点的切线场推导出矛盾。通过解决这些猜想，作者证明了采用足够高次数的通用多项式激活函数的神经网络是可识别的。 AI

排序理由该条目是发表在arXiv上的学术论文。[lever_c_demoted from research: ic=1 ai=0.4]

AI 生成摘要 · Google Gemini · 来自 1 个来源。我们如何撰写摘要 →

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arXiv cs.LG TIER_1 English(EN) · Xiaotian Chang, Yacoub Hendi · 2026-10-16 04:00

有界输入次数的多项式复合的线性无关性

arXiv:2610.20825v1 Announce Type: cross Abstract: We prove the weak composition-independence conjectures of Kohn, Marchetti, Massarenti and Mella. The proof uses deformations of rational curves and a single kernel of the linearized equation. Riemann-Roch gives a contradiction fro…